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layout: cv
permalink: /cv/
title: cv
description: Please click on the icon on the top right to download my CV if it does not show up in your browser.
nav: true
nav_order: 2
cv_pdf: cv.pdf
---
<div style="width: 100%; height:800">
<iframe src="https://filippomazzoli.github.io//assets/pdf/cv.pdf" width="100%" height="800">
Please click on the icon on the top right to download my CV if it does not show up in your browser.
</iframe>
<iframe src="https://filippomazzoli.github.io//assets/pdf/cv.pdf" width="100%" height="800"></iframe>
</div>
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---

<h3>Reading seminars</h3>
<ul>
<li>
<p><strong><em>Anosov representations</em></strong> (to appear): reading group at the <a href="https://www.virginia.edu">University of Virginia</a>, with <a href="https://sites.google.com/view/sara-maloni">Sara Maloni</a> and <a href="https://sites.google.com/view/alec-traaseth/home">Alec Traaseth</a>. Our main reference were <a href="http://www.math.lsa.umich.edu/~canary/">Dick Canary</a>'s "informal <a href="http://www.math.lsa.umich.edu/~canary/Anosovlecnotes.pdf">lecture notes</a>" on Anosov representations.</p>
</li>
<li>
<p><strong><em>A hyperKähler extension of Teichmüller space</em></strong>: <a href="https://math.uni.lu/geometry/reading_groups/index.html">G&T reading group</a> at the <a href="https://wwwen.uni.lu">Université du Luxembourg</a> in Fall 2018 and Spring 2019 semesters, organized by <a href="https://sites.google.com/site/mathbinbin/home">Binbin Xu</a> and presented by <a href="">Yan Mary He</a>, <a href="">Louis Merlin</a>, <a href="">Vincent Pecastaing</a>, <a href="">Andrea Seppi</a>, <a href="https://sites.google.com/site/mathbinbin/home">Binbin Xu</a>, and I. My main references were: Donaldson, <a href="https://www.intlpress.com/site/pub/files/_fulltext/journals/sdg/2003/0008/0001/SDG-2003-0008-0001-a006.pdf"><em>Moment maps in differential geometry</em></a>; Hodge, <a href="https://spiral.imperial.ac.uk/bitstream/10044/1/8115/1/Hodge-TWS-2005-PhD-Thesis.pdf"><em>Ph.D. thesis</em></a>; Trautwein, <a href="https://www.research-collection.ethz.ch/handle/20.500.11850/281862"><em>Ph.D. thesis</em></a>. Here are my notes:
<ul>
<li>
<a href="https://drive.google.com/file/d/11HHeSHCCoEdPEuA8oQx1pxtJ1hRt7IvE/view?usp=sharing">Part 1 - Outline and preliminaries on symplectic reduction</a>.
</li>
<li>
<a href="https://drive.google.com/file/d/118lrH2RTVBhQSP0ZS5P82dqwCTDALZs3/view?usp=sharing">Part 2 - Teichmüller space as symplectic quotient</a>.
</li>
<li>
<a href="https://drive.google.com/file/d/11Ogo9EfrAFFxZ9sZPtxBJRsb1Ajz92io/view?usp=sharing">Part 3 - The almost-Fuchsian deformation space</a>.
</li>
</ul>
</p>
<br>
<li>
<p><strong><em>Cannon-Thurston maps</em></strong>: <a href="https://math.uni.lu/geometry/reading_groups/index.html">G&T reading group</a> at the <a href="https://wwwen.uni.lu">Université du Luxembourg</a> in Spring 2020 semester, organized by <a href="http://www.normalesup.org/~acosta/">Miguel Acosta</a>, <a href="https://sites.google.com/site/mathbinbin/home">Binbin Xu</a>, and presented by <a href="http://www.normalesup.org/~acosta/">Miguel Acosta</a>, <a href="https://sites.google.com/view/diptaishikchoudhury">Diptaishik Choudhury</a>, <a href="https://sites.google.com/view/waiyeunglam/">Wai Yeung Lam</a>, <a href="https://math.uni.lu/~hanh/index.html">Thi Hanh Vo</a>, <a href="https://sites.google.com/site/mathbinbin/home">Binbin Xu</a>, and I. My main reference was: Cannon, Thurston, <a href="https://msp.org/gt/2007/11-3/p03.xhtml"><em>Group invariant Peano curves</em></a>. Here are my notes:
<ul>
<li>
<a href="https://drive.google.com/file/d/10zb1NJd_vyI5AlUjbmQoLLQ_1PlW6cR1/view?usp=sharing">Part 0 - Preliminaries</a>.
</li>
<li>
<a href="https://drive.google.com/file/d/11-uzzRZD6k8j-Y8s2vnkp6PuqC1_ruEA/view?usp=sharing">Part 1 - Outline of the proof</a>.
</li>
<li>
<a href="https://drive.google.com/file/d/11A-viucrlHtO05_b-2gvJnjCYo3x2NHK/view?usp=sharing">Part 2 - Pseudo-Anosov diffeomorphisms</a>.
</li>
</ul>
</p>
</li>
<br>
<h3>Some Math in Italian</h3>
<p><strong>Disclaimer!</strong> The material appearing below is a quite random collection of notes from my Master studies at the <a href="https://www.unipi.it">Università di Pisa</a>. These are NOT intended to be in any way complete references: bibliographies are not present or incomplete, they may very likely contain mistakes, and they have not been updated since I have taken these classes. Everyone is welcome to consult them, but at their own risk!
<ul>
<li>
<a href="https://drive.google.com/file/d/10h0O4yjzZiK8LCrGuxbVREu4iKH2AuBL/view?usp=sharing"><strong><em>Dehn filling iperbolico</em></strong></a>: notes from my exam of the course <em>Geometria iperbolica</em>, held by <a href="https://people.dm.unipi.it/martelli/">Bruno Martelli</a> at the <a href="https://www.unipi.it">Università di Pisa</a> in Fall 2015.<br />
</li>
<li>
<a href="https://drive.google.com/file/d/10g1_mz_N1k1GQHrNKi2DhhI35CLksl_X/view?usp=sharing"><strong><em>Cenni sui modelli geometrici in dimensione 3</em></strong></a>: notes from my exam of the course <em>3-Varietà</em>, held by <a href="https://people.dm.unipi.it/martelli/">Bruno Martelli</a> at the <a href="https://www.unipi.it">Università di Pisa</a> in Fall 2014.<br />
</li>
<li>
<a href="https://drive.google.com/file/d/10pZ_a_ssga4Zp8-mlOQIQmLSQZgvLVWY/view?usp=sharing"><strong><em>Il teorema di Cheng</em></strong></a>: notes from my exam of the course <em>Geometria Riemanniana</em>, held by <a href="http://cvgmt.sns.it/HomePages/cm/">Carlo Mantegazza</a> and <a href="https://sites.google.com/site/mazzierihome/">Lorenzo Mazzieri</a> at the Scuola Normale Superiore in Pisa in Fall 2014-Spring 2015.<br />
</li>
<li>
<a href="https://drive.google.com/file/d/10kPReXh5y4WmVyW6ClIdS4EyryY_3gFY/view?usp=sharing"><strong><em>Cenni sugli spazi dei moduli di superfici</em></strong></a>: notes from my exam of the course <em>Geometria e Topologia delle superfici</em>, held by <a href="https://people.dm.unipi.it/benedett/">Riccardo Benedetti</a> at the <a href="https://www.unipi.it">Università di Pisa</a> in Spring 2015.<br />
</li>
<li>
<a href="https://drive.google.com/file/d/10nTMvG9RDjzDU1yi5fzlMFL_ECSLl_-p/view?usp=sharing"><strong><em>Appunti di Topologia Algebrica</em></strong></a>: notes from the course <em>Topologia Algebrica</em>, held by <a href="https://people.dm.unipi.it/salvetti/index.html">Mario Salvetti</a> at the <a href="https://www.unipi.it">Università di Pisa</a> in Spring 2015. <a href="https://drive.google.com/file/d/10qi4kz4WoCzXeXMeTX5Llb2OLKZPKZ-E/view?usp=sharing">Here</a> you can also find some notes on Stiefel-Whitney and Chern classes from my exam.<br />
</li>
</ul>
<br>
<h3>Miscellaneous</h3>
<p>Here you can find my <a href="https://drive.google.com/file/d/10smOiltlBMaXMZtwzUHtg_7LrSCCx9jF/view?usp=sharing">Master thesis</a> on the representation theory of the quantum Teichmüller space. To every native English speaker: my sincerest apologies for having barbarically murdered your language at the time (fortunately I got a bit better at it now).<br />
### Reading seminars

+ ***Anosov representations*** (to appear): reading group at the [University of Virginia](https://www.virginia.edu), with [Sara Maloni](https://sites.google.com/view/sara-maloni) and [Alec Traaseth](https://sites.google.com/view/alec-traaseth/home). Our main reference were [Dick Canary](http://www.math.lsa.umich.edu/~canary/)'s "informal [lecture notes](http://www.math.lsa.umich.edu/~canary/Anosovlecnotes.pdf)" on Anosov representations.
+ ***A hyperKähler extension of Teichmüller space***: [G&T reading group](https://math.uni.lu/geometry/reading_groups/index.html) at the [Université du Luxembourg](https://wwwen.uni.lu) in Fall 2018 and Spring 2019 semesters, organized by [Binbin Xu](https://sites.google.com/site/mathbinbin/home) and presented by [Yan Mary He](), [Louis Merlin](), [Vincent Pecastaing](), [Andrea Seppi](), [Binbin Xu](https://sites.google.com/site/mathbinbin/home), and I. My main references were: Donaldson, _[Moment maps in differential geometry](https://www.intlpress.com/site/pub/files/_fulltext/journals/sdg/2003/0008/0001/SDG-2003-0008-0001-a006.pdf)_; Hodge, _[Ph.D. thesis](https://spiral.imperial.ac.uk/bitstream/10044/1/8115/1/Hodge-TWS-2005-PhD-Thesis.pdf)_; Trautwein, _[Ph.D. thesis](https://www.research-collection.ethz.ch/handle/20.500.11850/281862)_. Here are my notes:
+ [Part 1 - Outline and preliminaries on symplectic reduction](https://drive.google.com/file/d/11HHeSHCCoEdPEuA8oQx1pxtJ1hRt7IvE/view?usp=sharing).
+ [Part 2 - Teichmüller space as symplectic quotient](https://drive.google.com/file/d/118lrH2RTVBhQSP0ZS5P82dqwCTDALZs3/view?usp=sharing).
+ [Part 3 - The almost-Fuchsian deformation space](https://drive.google.com/file/d/11Ogo9EfrAFFxZ9sZPtxBJRsb1Ajz92io/view?usp=sharing).
+ ***Cannon-Thurston maps***: [G&T reading group](https://math.uni.lu/geometry/reading_groups/index.html) at the [Université du Luxembourg](https://wwwen.uni.lu) in Spring 2020 semester, organized by [Miguel Acosta](http://www.normalesup.org/~acosta/), [Binbin Xu](https://sites.google.com/site/mathbinbin/home), and presented by [Miguel Acosta](http://www.normalesup.org/~acosta/), [Diptaishik Choudhury](https://sites.google.com/view/diptaishikchoudhury), [Wai Yeung Lam](https://sites.google.com/view/waiyeunglam/), [Thi Hanh Vo](https://math.uni.lu/~hanh/index.html), [Binbin Xu](https://sites.google.com/site/mathbinbin/home), and I. My main reference was: Cannon, Thurston, _[Group invariant Peano curves](https://msp.org/gt/2007/11-3/p03.xhtml)_. Here are my notes:
+ [Part 0 - Preliminaries](https://drive.google.com/file/d/10zb1NJd_vyI5AlUjbmQoLLQ_1PlW6cR1/view?usp=sharing).
+ [Part 1 - Outline of the proof](https://drive.google.com/file/d/11-uzzRZD6k8j-Y8s2vnkp6PuqC1_ruEA/view?usp=sharing).
+ [Part 2 - Pseudo-Anosov diffeomorphisms](https://drive.google.com/file/d/11A-viucrlHtO05_b-2gvJnjCYo3x2NHK/view?usp=sharing).

---

### Some Math in Italian

**Disclaimer!** The material appearing below is a quite random collection of notes from my Master studies at the [Università di Pisa](https://www.unipi.it). These are NOT intended to be in any way complete references: bibliographies are not present or incomplete, they may very likely contain mistakes, and they have not been updated since I have taken these classes. Everyone is welcome to consult them, but at their own risk!

+ ***[Dehn filling iperbolico](https://drive.google.com/file/d/10h0O4yjzZiK8LCrGuxbVREu4iKH2AuBL/view?usp=sharing)***: notes from my exam of the course _Geometria iperbolica_, held by [Bruno Martelli](https://people.dm.unipi.it/martelli/) at the [Università di Pisa](https://www.unipi.it) in Fall 2015.
+ ***[Cenni sui modelli geometrici in dimensione 3](https://drive.google.com/file/d/10g1_mz_N1k1GQHrNKi2DhhI35CLksl_X/view?usp=sharing)***: notes from my exam of the course _3-Varietà_, held by [Bruno Martelli](https://people.dm.unipi.it/martelli/) at the [Università di Pisa](https://www.unipi.it) in Fall 2014.
+ ***[Il teorema di Cheng](https://drive.google.com/file/d/10pZ_a_ssga4Zp8-mlOQIQmLSQZgvLVWY/view?usp=sharing)***: notes from my exam of the course _Geometria Riemanniana_, held by [Carlo Mantegazza](http://cvgmt.sns.it/HomePages/cm/) and [Lorenzo Mazzieri](https://sites.google.com/site/mazzierihome/) at the Scuola Normale Superiore in Pisa in Fall 2014-Spring 2015.
+ ***[Cenni sugli spazi dei moduli di superfici](https://drive.google.com/file/d/10kPReXh5y4WmVyW6ClIdS4EyryY_3gFY/view?usp=sharing)***: notes from my exam of the course _Geometria e Topologia delle superfici_, held by [Riccardo Benedetti](https://people.dm.unipi.it/benedett/) at the [Università di Pisa](https://www.unipi.it) in Spring 2015.
+ ***[Appunti di Topologia Algebrica](https://drive.google.com/file/d/10nTMvG9RDjzDU1yi5fzlMFL_ECSLl_-p/view?usp=sharing)***: notes from the course _Topologia Algebrica_, held by [Mario Salvetti](https://people.dm.unipi.it/salvetti/index.html) at the [Università di Pisa](https://www.unipi.it) in Spring 2015. [Here](https://drive.google.com/file/d/10qi4kz4WoCzXeXMeTX5Llb2OLKZPKZ-E/view?usp=sharing) you can also find some notes on Stiefel-Whitney and Chern classes from my exam.

---

### Miscellaneous

Here you can find my [Master thesis](https://drive.google.com/file/d/10smOiltlBMaXMZtwzUHtg_7LrSCCx9jF/view?usp=sharing) on the representation theory of the quantum Teichmüller space. To every native English speaker: my sincerest apologies for having barbarically murdered your language at the time (fortunately I got a bit better at it now).
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layout: page
permalink: /research/
title: research
description: Still under construction
description: Click <a href="/publications/">here</a> to see the list of publications.
nav: true
nav_order: 5
---

### Some talks


+ <strong><em>Introduction to minimal surfaces and harmonic maps</em></strong>, Workshop "Minimal surfaces in symmetric spaces and Labourie's conjecture" in Autrans. August 22-26, 2022 ([notes](/assets/pdf/Slides talks/082122harmonic.pdf))
+ <strong><em>Shear-bend coordinates for pleated surfaces in PSL(d,C)</em></strong>, AMS-SMF-EMS Special Meeting in Grenoble. July 20, 2022 (<a href="/assets/pdf/Slides talks/072022shearbend.pdf">slides</a>).
+ <strong><em>A para-hyperKähler structure on the space of GHMC anti-de Sitter 3-manifolds</em></strong>, Heidelberg University. June 10, 2022 (<a href="/assets/pdf/Slides talks/061022parahyper.pdf">slides</a>).
+ <strong><em>Pleated surfaces for SO(2,n)-maximal representations</em></strong>, University of Virginia. April 5, 2022 (<a href="/assets/pdf/Slides talks/040522pleated.pdf">slides</a>).
+ <strong><em>Pleated surfaces for SO(2,n)-maximal representations</em></strong>, 55th Spring Topology & Dynamical Systems Conference. March 12, 2022 (<a href="https://drive.google.com/file/d/1-bLn86AweyDhBKDvSQJkbXeWCF-pSSJz/view?usp=sharing">recording</a>).
+ <strong><em>Infima of volumes of convex co-compact hyperbolic 3-manifolds</em></strong>, NCNGT 2021 Conference (<a href="https://www.youtube.com/watch?v=OFIMlu_Utg4&t=748s&ab_channel=FilippoMazzoli">recording</a>).
+ <strong><em>Constant Gaussian curvature surfaces in hyperbolic 3-manifolds</em></strong>, Pangolin seminar. November 3, 2020 (<a href="/assets/pdf/Slides talks/110320cgcsurfaces.pdf">slides</a>).
+ ***Introduction to minimal surfaces and harmonic maps***, Workshop "Minimal surfaces in symmetric spaces and Labourie's conjecture" in Autrans. August 22-26, 2022 ([notes](/assets/pdf/Slides talks/082122harmonic.pdf))
+ ***Shear-bend coordinates for pleated surfaces in PSL(d,C)***, AMS-SMF-EMS Special Meeting in Grenoble. July 20, 2022 ([slides](/assets/pdf/Slides talks/072022shearbend.pdf)).
+ ***A para-hyperKähler structure on the space of GHMC anti-de Sitter 3-manifolds***, Heidelberg University. June 10, 2022 ([slides](/assets/pdf/Slides talks/061022parahyper.pdf)).
+ ***Pleated surfaces for SO(2,n)-maximal representations***, University of Virginia. April 5, 2022 ([slides](/assets/pdf/Slides talks/040522pleated.pdf)).
+ ***Pleated surfaces for SO(2,n)-maximal representations***, 55th Spring Topology & Dynamical Systems Conference. March 12, 2022 ([recording](ttps://drive.google.com/file/d/1-bLn86AweyDhBKDvSQJkbXeWCF-pSSJz/view?usp=sharing)).
+ ***Infima of volumes of convex co-compact hyperbolic 3-manifolds***, NCNGT 2021 Conference ([recording](https://www.youtube.com/watch?v=OFIMlu_Utg4&t=748s&ab_channel=FilippoMazzoli)).
+ ***Constant Gaussian curvature surfaces in hyperbolic 3-manifolds***, Pangolin seminar. November 3, 2020 ([slides](/assets/pdf/Slides talks/110320cgcsurfaces.pdf)).

---

### Conferences co-organized

+ <a href="https://www.ncngt.org/">NCNGT 2022 Conference</a>, session on <em>Anosov representations</em> (co-organized with <a href="https://www.mathi.uni-heidelberg.de/~gviaggi/">Gabriele Viaggi</a>), September 19th-25th, 2022.
+ <a href="https://filippomazzoli.github.io/conferences/VTC2021/index.html">Virginia Topology Conference 2021</a> (co-organized with <a href="https://sites.google.com/view/koberdat">Thomas Koberda</a>, <a href="https://sites.google.com/view/sara-maloni">Sara Maloni</a>, and <a href="https://pengitore.weebly.com/">Mark Pengitore</a>), November 5th-7th, 2021.
+ [NCNGT 2022 Conference](https://www.ncngt.org/), session on _Anosov representations_ (co-organized with [Gabriele Viaggi](https://www.mathi.uni-heidelberg.de/~gviaggi/)), September 19th-25th, 2022.
+ [Virginia Topology Conference 2021](https://filippomazzoli.github.io/conferences/VTC2021/index.html) (co-organized with [Thomas Koberda](https://sites.google.com/view/koberdat), [Sara Maloni](https://sites.google.com/view/sara-maloni), and [Mark Pengitore](https://pengitore.weebly.com/)), November 5th-7th, 2021.

---

### REU Project (Summer 2021, University of Virginia)

<em>Katherine Betts, Troy Larsen, Jeffrey Utley, Avalon Vanis,</em> <strong><em>The Tri-Pants graph of the twice-punctured torus</em></strong>, preprint <a href="https://arxiv.org/abs/2111.07136">arXiv:2111.07136</a>.<br/>
_Katherine Betts, Troy Larsen, Jeffrey Utley, Avalon Vanis,_ ***The Tri-Pants graph of the twice-punctured torus***, preprint [arXiv:2111.07136](https://arxiv.org/abs/2111.07136).

##### Abstract:
We investigate the structure of the tri-pants graph, a simplicial graph introduced by Maloni and Palesi, whose vertices correspond to particular collections of homotopy classes of simple closed curves of the twice-punctured torus, called tri-pants, and whose edges connect two vertices whenever the corresponding pants differ by suitable elementary moves. In particular, by examining the relationship between the tri-pants graph and the dual of the Farey complex, we prove that the tri-pants graph is connected and it has infinite diameter.
**Abstract:** We investigate the structure of the tri-pants graph, a simplicial graph introduced by Maloni and Palesi, whose vertices correspond to particular collections of homotopy classes of simple closed curves of the twice-punctured torus, called tri-pants, and whose edges connect two vertices whenever the corresponding pants differ by suitable elementary moves. In particular, by examining the relationship between the tri-pants graph and the dual of the Farey complex, we prove that the tri-pants graph is connected and it has infinite diameter.

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